help for ^fracdiff^                

Generate fractionally-differenced timeseries --------------------------------------------

^fracdiff^ varname [^if^ exp] [^in^ range] D[real] [, ^GEN^erate(varn > ame)]

^fracdiff^ is for use with time-series data. You must ^tsset^ your data before > using ^fracdiff^; see help @tsset@. ^fracdiff^ supports the ^by^ prefix, which > may be used to operate on each time series in a panel. Alternatively, the ^if^ qualifier may be used to specify > a single time series in a panel.

Description -----------

^fracdiff^ computes a fractionally-differenced timeseries, given a value of the fractional integration (long memory) parameter ^d^. If a series exhibits long memory, it is neither stationary (I[0]) nor is it a unit root (I{1}) process; it is an I(d) process, with d a real number. An excellent survey of long memory models--which originated in hydrology, and have been widely applied in economics and finance-- is given by Baillie (1996).

Once one of several available estimators has been used to determine the ^d^ value for a timeseries, ^fracdiff^ may be used to generate the fractionally integrated transformation of the original series. Since this transformation involves applying an infinite-order lag distribution to the original series, the first twelve observations of the original series are used to provide starting values. ^fracdiff^ requires that there are no gaps, or missing values, within the specified sample. The resulting series will be named ^fracdiff^ by default, if that series name is not in use. The name of the new series may be specified with the ^generate^ option.

We illustrate ^fracdiff^ by using the GPH estimator (Geweke and Porter- Hudak, 1983) to estimate the fractional differencing parameter for a timeseries. The ^gphudak^ routine saves its point estimate of ^d^ in ^r(gph)^, which is then provided to the ^fracdiff^ routine.

Examples -------- . ^use http://fmwww.bc.edu/ec-p/data/Mills2d/fta.dta^ . ^gphudak ftap^ . ^fracdiff ftap,d(`r(gph)') gen(lmftap)^

References ----------

Baillie, R., Long Memory Processes and Fractional Integration in Econometrics, Journal of Econometrics, 73, 1996, 5-59. Geweke, J. and Porter-Hudak, S., The Estimation and Application of Long Memory Time Series Models, J. of Time Series Analysis, 1983, 221-238.

Author -------

Christopher F Baum, Boston College, USA baum@@bc.edu

Also see --------

On-line: help for @tsset@, @gphudak@ (if installed), @modlpr@ (if installed), @roblpr@ (if installed), @lomodrs@ (if installed)